U.S. patent application number 15/316813 was filed with the patent office on 2017-09-07 for metamaterial electromagnetic sensors for well logging measurements.
This patent application is currently assigned to HALLIBURTON ENERGY SERVICES, INC.. The applicant listed for this patent is HALLIBURTON ENERGY SERVICES, INC.. Invention is credited to Burkay DONDERICI, Ahmed E. FOUDA.
Application Number | 20170254917 15/316813 |
Document ID | / |
Family ID | 55218092 |
Filed Date | 2017-09-07 |
United States Patent
Application |
20170254917 |
Kind Code |
A1 |
FOUDA; Ahmed E. ; et
al. |
September 7, 2017 |
METAMATERIAL ELECTROMAGNETIC SENSORS FOR WELL LOGGING
MEASUREMENTS
Abstract
Metamaterials are used in well logging measurement tools to
position-shift and size-scale antennas such that they can be placed
very close to the outer perimeter of the tool, which can improve
azimuthal sensitivity and vertical resolution. Antennas of an
azimuthal pipe inspection or induction-based borehole imaging tool
can be placed with minimal stand-off against a borehole wall. Use
of such metamaterials can improve the resolution of logs or images
that are obtained by such tools. The metamaterials also can be used
to effectively centralize radial coils. Disclosed implementations
of metamaterials can be used with gradient ranging tools to
effectively increase the spacing between ranging antennas.
Increased spacing can maximize the signal levels with respect to
noise, without producing distortions that are observed with the
inclusion of magnetic materials.
Inventors: |
FOUDA; Ahmed E.; (Houston,
TX) ; DONDERICI; Burkay; (Houston, TX) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
HALLIBURTON ENERGY SERVICES, INC. |
Houston |
TX |
US |
|
|
Assignee: |
HALLIBURTON ENERGY SERVICES,
INC.
Houston
TX
|
Family ID: |
55218092 |
Appl. No.: |
15/316813 |
Filed: |
July 31, 2014 |
PCT Filed: |
July 31, 2014 |
PCT NO: |
PCT/US2014/049184 |
371 Date: |
December 6, 2016 |
Current U.S.
Class: |
1/1 |
Current CPC
Class: |
G01V 3/28 20130101 |
International
Class: |
G01V 3/28 20060101
G01V003/28 |
Claims
1. A well logging tool, comprising: a tool body; at least one
electromagnetic sensor with the tool body; a metamaterial coupled
to the tool body and the electromagnetic sensor that alters at
least one of an effective location and an effective size of the
sensor with respect to the tool body.
2. The well logging tool of claim 1, wherein the electromagnetic
sensor is embedded in the metamaterial.
3. The well logging tool of claim 1, wherein the electromagnetic
sensor is outside the metamaterial.
4. The well logging tool of claim 1, wherein the electromagnetic
sensor is physically located along a central axis of the tool.
5. The well logging tool of claim 4, wherein the metamaterial is
designed to position shift the electromagnetic sensor towards a
periphery of the tool body.
6. The well logging tool of claim 1, wherein the electromagnetic
sensor is physically located away from a central axis of the
tool.
7. The well logging tool of claim 6, wherein the metamaterial is
designed to position shift the electromagnetic sensor towards a
center of the tool body.
8. The well logging tool of claim 1, wherein the metamaterial is
embedded in the tool body.
9. The well logging tool of claim 1, wherein the metamaterial is
coupled to the tool via a deployable arm.
10. The well logging tool of claim 1, further comprising at least a
second electromagnetic sensor coupled to the metamaterial, where
the first electromagnetic sensor is position shifted to a first
position, and the second electromagnetic sensor is position shifted
to the first or to the second position.
11. The well logging tool of claim 10, further comprising at least
a third electromagnetic sensor coupled to the metamaterial, where
the third electromagnetic sensor is position shifted to the first,
to the second, or to a third position.
12. The well logging tool of claim 11, wherein the electromagnetic
sensors comprise a triaxial coil.
13. The well logging tool of claim 1, wherein the metamaterial is
designed to shrink the effective size of the electromagnetic
sensor.
14. The well logging tool of claim 13, wherein the electromagnetic
sensor comprises a coil.
15. The well logging tool of claim 1, wherein the electromagnetic
sensor comprises a coil.
16. A method of designing a well logging tool, comprising:
constructing a metamaterial having unit cells in a configuration
providing at least one of a position-shifting function with respect
to electromagnetic radiation passing through the metamaterial, and
a size-shrinking function with respect to an electromagnetic
sensor; locating the electromagnetic sensor in operative
relationship with the constructed metamaterial; and providing the
electromagnetic sensor and metamaterial in a tool body.
17. The method of claim 16, further comprising constructing the
metamaterial having unit cells in a configuration providing size
scaling of said electromagnetic sensor.
18. The method of claim 16, wherein the metamaterial is designed to
position-shift the effective location of the electromagnetic sensor
towards a periphery of the tool body.
19. The method of claim 16, wherein the electromagnetic sensor is
embedded in the metamaterial.
20. A method of designing a well logging tool, comprising:
constructing a metamaterial having unit cells in a configuration
providing a size-shrinking function with respect to an
electromagnetic sensor; locating the electromagnetic sensor in
operative relationship with the constructed metamaterial; and
providing the electromagnetic sensor and metamaterial in a tool
body.
Description
FIELD
[0001] The subject matter herein generally relates to sensors for
use in well logging applications such as induction-based borehole
imaging and azimuthal pipe inspection tools. In particular, the
disclosure relates to the use of metamaterials in the design of
such sensors to compensate for the restrictive geometries exhibited
by existing tools.
BACKGROUND
[0002] In induction-based borehole imaging and azimuthal pipe
inspection tools, it is usually desirable to place the sensors as
close as possible to the outer perimeter of the tool to improve
azimuthal sensitivity. However, the minimum achievable stand-off is
determined by the finite cross-section of the sensor. In principle,
the stand-off cannot be smaller than the radius of the sensor.
Likewise, it is desirable to squeeze the sensor in the axial
direction to improve vertical resolution. Again, this is limited by
the physical dimensions of the coil windings.
[0003] In a similar sense, the spacing between coils in gradient
ranging tools is determined by the geometry of the coils. In these
tools, it is desirable to maximize the aperture spanned by the
ranging coils (in other words, the spacing between the coils) so as
to improve the gradient stability in the presence of measurement
noise. Conventional ways to expand the effective aperture include
inserting high-k dielectric materials, (materials having a high
dielectric constant), or high-.mu. magnetic materials, (materials
having a high magnetic constant), between the coils. However, the
intrinsic impedances of such high index of refraction materials are
essentially different from the impedances of the operating ambient
background. This impedance difference introduces signal distortions
that must be compensated.
BRIEF DESCRIPTION OF THE DRAWINGS
[0004] Implementations of the present technology will now be
described, by way of example only, with reference to the attached
figures, wherein:
[0005] FIGS. 1A-1D are diagrams illustrating the principles of
transformation optics which are used in the design of
metamaterials;
[0006] FIGS. 2A-2B are diagrams illustrating the composition of
conventional materials versus metamaterials;
[0007] FIG. 3A is a diagram of a multi-cylinder split ring
resonators SRR metamaterial;
[0008] FIG. 3B is a diagram of a directive metamaterial
antenna;
[0009] FIG. 4 is a diagram of a negative index of refraction (NIR)
lens in which double negative (DNG) metamaterial lens is
employed;
[0010] FIGS. 5A-5B are diagrams of a capacitively loaded
metamaterial SNG flat lens;
[0011] FIG. 5C shows a capacitively loaded metamaterial single
negative SNG cylindrical rolled-up lens;
[0012] FIG. 6 is a diagram of a DNG chiral metamaterial;
[0013] FIGS. 7A-7B are diagrams illustrating a decentralized
antenna design in accordance with an embodiment of the present
disclosure;
[0014] FIGS. 8A-8B are graphs illustrating the coordinate
transformation of the embodiment in FIG. 7;
[0015] FIGS. 9A-9D are diagrams illustrating a decentralized
antenna design in accordance with another embodiment of the present
disclosure;
[0016] FIGS. 10A-10B are diagrams illustrating a decentralized and
scaled antenna design in accordance with yet another embodiment of
the present disclosure;
[0017] FIGS. 11A-11B are graphs illustrating the coordinate
transformation of the design in FIG. 10;
[0018] FIGS. 12A-12B are diagrams illustrating a design of an
antenna for borehole casing inspection in accordance with another
embodiment of the present disclosure;
[0019] FIGS. 13A-13B are diagrams illustrating a design of a
borehole imaging tool with a backbone in accordance with another
embodiment of the present disclosure;
[0020] FIGS. 13C-13D are graphs illustrating the coordinate
transformation of the design in FIGS. 13A-13B;
[0021] FIGS. 14A-14B are diagrams illustrating a design of a
borehole imaging tool with a triaxial coil in accordance with
another embodiment of the present disclosure;
[0022] FIGS. 14C-14D are graphs illustrating the coordinate
transformation of the design in FIGS. 14A-14B;
[0023] FIGS. 15A-15B are diagrams illustrating a design of a
borehole imaging tool that collapses any internally placed
arbitrary source to a centralized point source in accordance with
another embodiment of the present disclosure;
[0024] FIGS. 15C-15D are graphs illustrating the coordinate
transformation of the design in FIGS. 15A-15B;
[0025] FIGS. 16A-16B are diagrams illustrating a design of a
gradient range measuring tool in accordance with another embodiment
of the present disclosure;
[0026] FIG. 17 is a diagram illustrating an example environment for
a tool employing metamaterial lens in accordance with the
principles of the present disclosure; and
[0027] FIG. 18 is a diagram illustrating an example wireline
environment for a tool employing metamaterial lens in accordance
with the principles of the present disclosure.
DETAILED DESCRIPTION
[0028] It will be appreciated that for simplicity and clarity of
illustration, where appropriate, reference numerals have been
repeated among the different figures to indicate corresponding or
analogous elements. In addition, numerous specific details are set
forth in order to provide a thorough understanding of the
embodiments described herein. However, it will be understood by
those of ordinary skill in the art that the embodiments described
herein can be practiced without these specific details. In other
instances, methods, procedures and components have not been
described in detail so as not to obscure the related relevant
feature being described. Also, the description is not to be
considered as limiting the scope of the embodiments described
herein. The drawings are not necessarily to scale and the
proportions of certain parts have been exaggerated to better
illustrate details and features of the present disclosure.
[0029] In the following description, terms such as "upper,"
"upward," "lower," "downward," "above," "below," "downhole,"
"uphole," "longitudinal," "lateral," and the like, as used herein,
are descriptive of a relationship with, and are used with reference
to, the bottom or furthest extent of the surrounding wellbore, even
though the wellbore or portions of it may be deviated or
horizontal. Correspondingly, the transverse, axial, lateral,
longitudinal, radial, etc., orientations shall mean orientations
relative to the orientation of the surrounding wellbore or wellbore
tool in question. Additionally, the non-limiting embodiments within
this disclosure are illustrated such that the orientation is such
that the right-hand side is down hole compared to the left-hand
side.
[0030] Several definitions that apply throughout this disclosure
will now be presented.
[0031] The term "coupled" is defined as connected and/or attached,
whether directly or indirectly through intervening components, and
is not necessarily limited to physical connections. The connection
can be such that the objects are permanently connected or
releasably connected. The term "outside" refers to a region that is
beyond the outermost confines of a physical object. The term
"inside" indicate that at least a portion of a region is partially
contained within a boundary formed by the object. The term
"substantially" is defined to be essentially conforming to the
particular dimension, shape or other word that substantially
modifies, such that the component need not be exact. For example,
substantially cylindrical means that the object resembles a
cylinder, but can have one or more deviations from a true
cylinder.
[0032] The term "radially" means substantially in a direction along
a radius of the object, even if the object is not exactly circular
or cylindrical.
[0033] The term "axially" means substantially along a direction of
the axis of the object. If not specified, the term axially is such
that it refers to the longer axis of the object.
[0034] "Processor" as used herein is an electronic circuit that can
make determinations based upon inputs and is interchangeable with
the term "controller". A processor can include a microprocessor, a
microcontroller, and a central processing unit, among others. While
a single processor can be used, the present disclosure can be
implemented over a plurality of processors, including local
controllers in a tool or sensors along the drill string.
[0035] The present disclosure is described in relation to
metamaterials. Metamaterials are artificially-engineered composites
that inherit their electrical properties from the geometry and
arrangement of their constituting unit cells. Metamaterials can be
realized in many different ways depending on the operation
frequency. Metamaterials designed according to transformation
optics rules exhibit iso-impedance; in other words metamaterials
have substantially the same intrinsic impedance as the background
medium, and therefore introduce substantially no spurious
reflections, as opposed to more conventional materials. In
addition, metamaterials can be designed to control electromagnetic
fields in ways not achievable by conventional materials.
[0036] The metamaterial realization techniques described herein
employ resonant structures. This makes the metamaterial highly
dispersive and lossy when operated near resonance. This also means
that a metamaterial with given properties can only be designed to
operate at a single frequency. The use of metamaterials also
extends to quasi-static and DC applications, such as for a DC
diamagnetic metamaterial, for a DC magnetic cloak, and for a DC
electric concentrator. Negative index of refraction metamaterial
can also be used in enhanced material investigation tools. The
metamaterial focuses electromagnetic energy for deeper depth of
investigation yielding more efficient use of the available power.
One use includes an electromagnetic measurement tool within a
borehole that measures formation properties associated with oil
exploration.
[0037] According to the present disclosure, metamaterials can be
advantageous in well logging electromagnetics for a number of
reasons. Metamaterials enable narrow band, single-frequency
operation of most tools relevant to this disclosure. Metamaterials
accommodate the regular cylindrical geometry of most tools relevant
to this disclosure. The generally low operating frequencies of such
tools enhance the application of the homogenization condition
described above. Furthermore, electric and magnetic fields are
decoupled in many tools relevant to this disclosure; this decoupled
relationship facilitates the realization of metamaterials using a
reduced set of material properties.
[0038] Another reason that metamaterials can be advantageous in
well logging electromagnetics is that the predefined field
polarization of most tools relevant to this disclosure facilitates
the design of an appropriate metamaterial using a reduced set of
parameters. Additionally, if SNG and DNG are not needed,
non-resonant, low loss metamaterials operating at wavelengths much
longer than the unit cell can be designed.
[0039] According to the present disclosure, the constraining
geometries in well logging can be alleviated by introducing
appropriate spatial transformations realized using metamaterials.
In accordance with the present disclosure, metamaterials are
designed to achieve position shifting and scaling of
electromagnetic sensors in wellbores. This alters the effective
location and effective size of the electromagnetic sensors, making
them appear smaller and/or in a different position than their
respective actual size and actual location. This is applicable to
any electromagnetic sensor used in wellbores, for example
electromagnetic coils.
[0040] In one embodiment of the disclosure, the stand-off between
the sensors and the tool body in azimuthal pipe inspection and
induction-based borehole imaging tools is minimized through the use
of position shifting metamaterials. In particular, the metamaterial
"shrinks" the actual sensors into down-scaled equivalents that are
then virtually shifted towards the outer perimeter of the tool.
This serves to increase both azimuthal and vertical resolutions of
inspection and imaging tools. In another embodiment, transformation
metamaterial is used to effectively displace the tool backbone
allowing radial coils to be effectively positioned at the center of
the tool. In this way, a centralized triaxial coil can be realized
using three decentralized coils. In yet another embodiment, the
spacing between coils in gradient ranging tools is expanded by the
use of metamaterials. Such expansion increases the stability of the
measured gradient to noise and other measurement uncertainties.
[0041] FIGS. 1A-1D conceptually illustrate metamaterials. FIG. 1A
shows an original two-dimensional space defined by a grid. If it is
assumed that the underlying grid is "elastic" and can be
transformed to achieve certain field shaping as shown in FIG. 1B,
the form-invariance of Maxwell's equations under coordinate
transformation means that such transformations can be interpreted
as if the original medium within the transformed space is replaced
by a generally anisotropic and inhomogeneous medium. Materials
having such properties may not exist in nature and therefore are
referred to as "metamaterials." A well-known application of
transformation optics by metamaterials is invisibility cloaking. As
shown in FIG. 1C, the original grid space is transformed to create
an enclosure in the inner region (.rho.<R.sub.1) while
maintaining the original grid in the outer region
(.rho.>R.sub.2.) The region where (R.sub.1<.rho.<R.sub.2)
is the region in which one or more metamaterial is used to mimic
the illustrated grid deformation. This deformation allows light
rays to be smoothly steered around the enclosure in the inner
region, rendering invisible any object placed in the enclosure. A
three-dimensional depiction of such cloaking is shown in FIG.
1D.
[0042] Mathematically, transformation optics can be described using
Maxwell's equations. In the original space, we have the
equations:
.gradient..times.E=-j.omega..mu.H
.gradient..times.H=j.omega..di-elect cons.E+J.sub.s (1)
[0043] Given the following spatial transformation in cylindrical
coordinates:
.rho.'=.rho.'(.rho.,.phi.,Z)
.phi.'=.phi.'(.rho.,.phi.,Z)
Z'=Z'(.rho.,.phi.,Z)
[0044] Maxwell's equations take the following form, as they are
form-invariant under coordinate transformation:
.gradient.'.times.E'=-j.omega..mu.'H'
.gradient.'.times.H'=j.omega..di-elect cons.'E'+J'.sub.s (3)
where
.mu. ' = A .mu. A T A .epsilon. ' = A .epsilon. A T A J s ' = AJ s
J s AJ s ( 4 ) and [ .differential. .rho. ' .differential. p
.differential. .rho. ' .rho. .differential. .phi. .differential.
.rho. ' .differential. z .rho. ' .differential. .phi. '
.differential. .rho. .rho. ' .differential. .phi. ' .rho.
.differential. .phi. .rho. ' .differential. .phi. ' .differential.
z .differential. z ' .differential. .rho. .differential. z ' .rho.
.differential. .phi. .differential. z ' .differential. z ] ( 5 )
##EQU00001##
is the Jacobian matrix of the transformation.
[0045] The above equations (4) represent the material properties
and the equivalent current source that should be used to realize
the prescribed coordinate transformation. Transformations that
preserve grid continuity across the transformed space boundary
result in reflectionless, iso-impedance metamaterials. Another
class of transformations exists, called embedded transformations,
in which the grid continuity is broken and therefore reflectionless
transmission across the metamaterial/background medium interface is
not guaranteed. However, embedded transformations provide higher
degrees of flexibility for manipulating fields outside the
metamaterial device, and can be designed in such a way to minimize
spurious reflections.
[0046] Thus, as conceptually shown in FIG. 2A, while conventional
materials attain their macroscopic properties from the chemical
composition of their constituting atoms, metamaterials as
conceptually shown in FIG. 2B attain their macroscopic properties
from their artificially engineered constituting unit cells.
Metamaterials have been realized in many different ways depending
on the application and frequency of operation. Examples of
metamaterials summarized below demonstrate their practical
feasibility in the current applications.
[0047] FIG. 3A shows a metamaterial constructed in the form of
concentric cylinders having split ring resonators (SRRs) printed
thereon. A two-dimensional invisibility cloak requires the radial
component of the permeability tensor (.mu..sub.rr) to vary radially
as shown in the inset of FIG. 3A. The dimensions of the SRRs are
adjusted in each cylinder to achieve the required profile. In order
to describe the assembly of SRRs with effective macroscopic
material properties, the dimension of the unit cell must be much
smaller than the desired operating wavelength, which is known in
the art as the homogenization condition. Nevertheless, the
dimension of the SRR must be large enough to resonate at or near
the operating frequency.
[0048] FIG. 3B shows an example metamaterial wherein a directive
antenna is realized using alternating electric and magnetic
metamaterial layers. The electric layers realize the shown discrete
.di-elect cons..sub.zz profile using five sets of electric-LC (ELC)
resonators. The magnetic layers realize the shown discrete
.mu..sub.yy profile using SRRs.
[0049] Another example metamaterial construct is shown in FIG. 4.
This figure illustrates a negative index of refraction (NIR) lens,
in which double negative (DNG) metamaterials are used. Negative
permeability is realized using SRRs, whereas negative permittivity
is realized using thin wires.
[0050] At lower operating frequencies, the dimensions of the SRRs
and ELCs which are required in order to resonate at the operating
frequency become prohibitively large for practical implementation.
For such frequencies, lumped components can be used to achieve
resonance without increasing the unit cell size. An example of
single negative (SNG) lenses is shown in FIGS. 5A-5C, wherein FIG.
5A shows a flat SNG lens in its operative configuration, FIG. 5B
shows the internal capacitor unit cell structure and FIG. 5C shows
a cylindrical rolled-up SNG lens. SNG lenses have been used to
enhance the sensitivity and spatial resolution of RF coils in
magnetic resonance imaging (MRI) systems.
[0051] FIG. 6 shows an example of an alternative design of DNG
metamaterials involving chiral materials. A chiral metamaterial is
constructed of insulated metal strips wound in a helix shape, with
the individual helixes stacked in a three-dimensional (3-D)
arrangement to form an isotropic DNG structure. The unit cells (in
other words, chiral helixes) can have internal resonances with
dimensions on the order of 1/1000 (one thousandth) of the operating
wavelength. This characteristic is particularly important in the
design of metamaterials operating at very low frequencies (in other
words, quasi-static metamaterials).
[0052] FIGS. 7A and 7B show one embodiment of the disclosure in the
form of an induction-based borehole imaging tool. FIG. 7A shows the
desired virtual design. A tool having a tool body 1 is inserted
into a borehole 3 of a formation 4 and relatively positioned using,
for instance, a deployable arm 5. A conveyance 2 is centrally
disposed relative to the tool body 1 and upon which the tool body 1
can be suspended. The conveyance 2 can be a wireline, toolstring,
coiled tubing, slickline, cables, E-line, or the like (see FIG. 18
regarding an exemplary wireline conveyance). An electromagnetic
sensor, namely, eccentric coil 6 is desirably disposed adjacent to
the borehole wall. It is desirable to reduce the stand-off between
the coil 6 and the borehole walls to improve azimuthal resolution.
In implementation, however, the restrictive dimensions of such a
tool render such configuration infeasible. Using the transformation
optic principles of metamaterials, as shown in FIG. 7B, an actual
electromagnetic sensor, namely, concentric coil 7 is embedded in a
metamaterial 8. In at least one embodiment within this disclosure,
metamaterial 8 can be located in a moveable pad which is coupled to
the tool via a deployable arm 5. The metamaterial 8 is designed
such that the electromagnetic fields produced by the concentric
coil 7 outside the tool body are identical to fields that would be
produced by the eccentric coil 6 of FIG. 7A. Accordingly, the use
of the metamaterial 8 alters the effective location of the coil 7
so that although actually being located near the middle portion of
the tool body 1 as shown in FIG. 7B, it produces magnetic fields as
if it were located the periphery of the tool body as shown in FIG.
7A.
[0053] One possible coordinate transformation is shown in FIGS. 8A
and 8B. As shown, the grid is kept intact outside the metamaterial,
indicating that the fields produced by the embedded concentric coil
are identical to fields produced by an eccentric coil embedded in
an ambient medium. The transformation involves both source and
material transformations. The moments of the concentric and
(virtual) eccentric coils are related through equation (4) above. A
typical operating frequency range of this tool is from 250 Hz to 10
GHZ, which lies within the range of practical implementation of
metamaterials. Accordingly, the actual source 13 placed at an
arbitrary position is altered such that its effective location is
changed to an effective centralized point source 14 as shown in
FIG. 8A.
[0054] FIGS. 9A-9D show an alternate embodiment of the tool of FIG.
7, wherein the concentric coil 7 is placed outside a metamaterial
pad 8 that shrinks the space between the coil and the outer
perimeter of the tool body 1. By shrinking the space between the
coil 7 and the outer perimeter of the tool body 1, the effective
location of the coil 7 is altered such that although its actual
location is near the center of the tool body, its virtual position
is closer to the perimeter of the tool body 1. In this case, the
continuity of grid lines across the top and bottom faces of the
metamaterial is broken, which causes signal distortions near those
faces. Nevertheless, this embodiment has the advantage that the
coil does not need to be embedded inside the metamaterial, which
provides more design freedom in realizing the metamaterial.
Moreover, signal distortions at or near the interface of the
metamaterial and the tool body can be neglected, since high
resolution shallow measurements are of interest in this
application.
[0055] In yet another embodiment as shown in FIGS. 10A-10B, the
metamaterial is used to downscale a larger concentric coil 7 to
mimic a virtual smaller eccentric coil 6. The metamaterial
downscales the coil 7 both radially and axially, and decentralizes
the downscaled coil. Radial downscaling enables a stand-off smaller
than the radius of the actual coil, whereas axial downscaling
yields better vertical resolution than that achievable by the
actual coil.
[0056] FIGS. 11A and 11B illustrate one possible coordinate
transformation to achieve the combined downscaling/position
shifting effect. It is to be noted that the point source at the
center of the original (virtual) space is transformed into a
finite-volume region in the transformed (actual) space. Any
arbitrary sized source placed inside this finite-volume enclosure
and surrounded by the proper transformation metamaterial will
produce the identical fields outside the metamaterial as the
(virtual) eccentric point source, thereby changing the effective
location of the source.
[0057] FIGS. 12A and 12B illustrate a further embodiment of the
disclosure in which the downscaling/position shifting
transformation is applied to an azimuthal pipe or casing inspection
tool. As shown in FIG. 12A, an ideal (virtual) design is to have a
coil 6 in a dielectric pad 19 such that the coil 6 is adjacent to
the wall of a borehole casing 9 in a borehole 3 and small enough to
detect small faults 16 in the casing. Therefore, the effective
location and size is altered in the ideal (virtual) design as
compared to its actual location and size. The pad 19 is pressed
against the wall 122 of the casing 9 by a deployable arm 5
connected to the tool body 1. As shown in FIG. 12B, the actual
design uses a coil 7 which is of larger dimensions than the ideal
coil 6, centrally embedded in a metamaterial pad 20. Therefore, the
effective size of coil 7 is altered, and in particular, reduced as
compared to its actual size. Moreover, the location of the coil 7
is also altered and shifted toward the borehole casing. Again,
minimal stand-off between the coil 7 and the wall 122 and small
coil height are desirable to resolve small faults in the casing
under inspection. Appropriately designing the metamaterial pad in
accordance with the transformation principles explained above will
result in the actual coil 10 of FIG. 12B being mapped to the ideal
(virtual) coil equivalent as shown in FIG. 12A.
[0058] FIGS. 13A and 13B show another embodiment wherein the
scaling-shifting transformation is used in an induction logging
tool having a tool backbone 11 as shown in FIG. 13B, to effectively
shift the location of an eccentric coil 7 to the center of the tool
in place of the tool backbone 11, as shown in FIG. 13A as virtual
coil 6. This is accomplished by embedding the tool backbone 11 in
an appropriately designed metamaterial 8. The backbone 11 lies
inside a finite-volume enclosure of the transformed grid, as shown
in FIG. 13D, thereby transforming it to an infinitesimal eccentric
line while the coil 7 is positioned so as to be shifted to be
axially located in the tool. The resulting equivalent image is a
centralized radial coil radiating in the presence of an
infinitesimally thin eccentric backbone, as shown in FIG. 13C.
[0059] FIGS. 14A and 14B show yet another embodiment of an
induction logging tool in which a virtual centralized triaxial coil
6 (FIG. 14A) is realized using three decentralized coils 7a, 7b, 7c
embedded in a position-shifting metamaterial 8 (FIG. 14B). Again,
the tool backbone 11 is effectively shrunk to an infinitesimal line
by being placed in an enclosure within the metamaterial. The
metamaterial further effectively co-locates the three coils 7a, 7b,
7c at a single point on the tool axis, thus changing their
effective locations, as shown in FIG. 14A. Thus, while conventional
triaxial coils consist of three electrically coupled pairs of
orthogonal coils, the use of a metamaterial enables the realization
of a triaxial coil by using only three uncoupled orthogonal coils.
FIGS. 14C and 14D illustrate the corresponding grid
transformations.
[0060] FIGS. 15A and 15B illustrate an embodiment in which the same
metamaterial 8 of FIG. 14B is used to create a position-independent
source space 12. Any source 13 placed at an arbitrary position
within the enclosure 12 effectively collapses to an effective
centralized point source 14 as shown in FIG. 15A, as a result of
the coordinate transformation achieved by the metamaterial 8. The
moment of the effective point source 14 is dependent upon the
position of the actual source 13 inside the enclosure 12, which can
be easily calibrated. This embodiment is important for applications
where accurate placement and maintenance of source position with
respect to the tool body 1 is required. FIGS. 15C and 15D
illustrate the corresponding grid transformation.
[0061] FIGS. 16A and 16B illustrate an embodiment of the disclosure
relating to a gradient ranging tool. In such a tool having a tool
body 1, two coils 7a, 7b are used to measure the azimuthal magnetic
field that is generated by a current-carrying casing 9. In the
figures, current is represented by arrow 10. The casing is embedded
in a formation 4. The tool body 1 is placed in a ranging borehole 3
substantially parallel to the casing 9 in formation 4. The outputs
of the coils 7a, 7b are differenced to compute the magnetic field
gradient. To increase the stability of the gradient measurement in
the presence of measurement noise/errors, it is desirable to
maximize the spacing between the two coils (or aperture spanned by
the two coils). This is shown in FIG. 16A as coils 6. However, the
maximum attainable spacing within a given tool is determined by the
size of the coils. This limitation is alleviated by embedding coils
7a, 7b as shown in FIG. 16B in a two-enclosure size
scaling/position shifting metamaterial 8, which effectively shrinks
the coils in size and shifts their effective location along
opposite sides of the tool perimeter.
[0062] As noted above, and illustrated in FIG. 17, in a working
environment the tool having a tool body 1 can be used in part of a
drilling, logging or other operation where the tool is used
downhole. A wellbore 148 is shown that has been drilled into the
earth 154 from the ground's surface 127 using a drill bit 22. The
drill bit 22 is located at the bottom, distal end of the drill
string 132 and the bit 22 and drill string 132 are being advanced
into the earth 154 by the drilling rig 129. The drilling rig 129
can be supported directly on land as shown or on an intermediate
platform if at sea. For illustrative purposes, the top portion of
the well bore includes casing 134 that is typically at least
partially comprised of cement and which defines and stabilizes the
wellbore after being drilled.
[0063] As shown in FIG. 17, the drill string 132 supports several
components along its length. A sensor sub-unit 152 is shown for
detecting conditions near the drill bit 22, conditions which can
include such properties as formation fluid density, temperature and
pressure, and azimuthal orientation of the drill bit 22 or string
132. In the case of directional drilling, measurement while
drilling (MWD)/logging while drilling (LWD) procedures are
supported both structurally and communicatively. The instance of
directional drilling is illustrated in FIG. 17. The tool body 1 may
also be deployed by wireline conveyance 130 or coiled tubing 178 as
an independent service up removal of drill string 132 (wireline
conveyance 130 further illustrated in FIG. 18 as discussed
below).
[0064] In the example of FIG. 17, the lower end portion of the
drill string 132 can include a drill collar proximate the drilling
bit 22 and a rotary steerable drilling device 120. The drill bit 22
may take the form of a roller cone bit or fixed cutter bit or any
other type of bit known in the art. The sensor sub-unit 152 is
located in or proximate to the rotary steerable drilling device 120
and advantageously detects the azimuthal orientation of the rotary
steerable drilling device 120. Other sensor sub-units 135, 136 are
shown within the cased portion of the well which can be enabled to
sense nearby characteristics and conditions of the drill string,
formation fluid, casing and surrounding formation. Regardless of
which conditions or characteristics are sensed, data indicative of
those conditions and characteristics is either recorded downhole,
for instance at the processor 144 for later download, or
communicated to the surface either by wire using repeaters 137,139
up to surface wire 172, or wirelessly or otherwise. If wirelessly,
the downhole transceiver (antenna) 138 can be utilized to send data
to a local processor 18, via topside transceiver (antenna) 114.
There the data may be either processed or further transmitted along
to a remote processor 112 via wire 116 or wirelessly via antennae
114 and 110.
[0065] The possibility of an additional mode of communication is
contemplated using drilling mud 140 that is pumped via conduit 142
to a downhole mud motor 176. The drilling mud is circulated down
through the drill string 132 and up the annulus 133 around the
drill string 132 to cool the drill bit 22 and remove cuttings from
the wellbore 148. For purposes of communication, resistance to the
incoming flow of mud can be modulated downhole to send backpressure
pulses up to the surface for detection at sensor 174, and from
which representative data is sent along communication channel 121
(wired or wirelessly) to one or more processors 118, 112 for
recordation and/or processing.
[0066] The sensor sub-unit 152 is located along the drill string
132 above the drill bit 22. The sensor sub-unit 136 is shown in
FIG. 17 positioned above the mud motor 176 that rotates the drill
bit 22. Additional sensor sub-units 135, 136 can be included as
desired in the drill string 132. The sub-unit 152 positioned below
the motor 176 communicates with the sub-unit 136 in order to relay
information to the surface 127.
[0067] A surface installation 119 is shown that sends and receives
data to and from the well. The surface installation 119 can
exemplarily include a local processor 118 that can optionally
communicate with one or more remote processors 112, 117 by wire 116
or wirelessly using transceivers 110, 114.
[0068] In alternative examples, due to increased power
requirements, or desire for reduced vibration resulting from a
drill string, or other reasons, the tool having tool body 1 can be
employed with "wireline" systems as illustrated in FIG. 18 in order
to carry out logging or other operations. For example, instead of
using the drill string 132 of FIG. 17 to lower tool body 1, it can
be lowered into the wellbore 148 by wireline conveyance 130 as
shown in FIG. 18. The wireline conveyance 130 can be anchored in
the drill rig 129 or portable means such as a truck. The wireline
conveyance 130 can be one or more wires, cables, or the like. The
illustrated wireline conveyance 130 provides support for the tool,
as well as enabling communication between the tool processors on
the surface and providing a power supply. For example, the wireline
conveyance 130 is sufficiently strong and flexible to tether the
tool body 1 through the wellbore 148, while also permitting
communication through the wireline conveyance 130 to local
processor 118 and/or remote processors 112, 117. Additionally,
power can be supplied via the wireline conveyance 130 to meet power
requirements of the tool.
[0069] Further, as discussed above with respect to FIGS. 7-16, the
tool body 1 is depicted as being deployed on a conveyance 2, which
may include the wireline conveyance 130 shown in FIG. 18.
Accordingly, logging operations can be conducted by the tool body 1
via wireline in accordance with the disclosure herein.
[0070] Numerous examples are provided herein to enhance
understanding of the present disclosure. A specific set of examples
are provided as follows. In a first example, there is disclosed
herein a well logging tool, including a tool body (1); at least one
electromagnetic sensor (7) with the tool body; a metamaterial (8)
coupled to the tool body and the electromagnetic sensor that alters
at least one of an effective location and an effective size of the
sensor (7) with respect to the tool body (1).
[0071] In a second example, there is disclosed herein a method
according to the first example wherein the electromagnetic sensor
(7) is embedded in the metamaterial (8).
[0072] In a third example, there is disclosed herein a method
according to the first or second examples, wherein the
electromagnetic sensor (7) is outside the metamaterial (8).
[0073] In a fourth example, there is disclosed herein a method
according to any of the preceding examples first to the third,
wherein the electromagnetic sensor (7) is physically located along
a central axis of the tool.
[0074] In a fifth example, there is disclosed herein a method
according to any of the preceding examples first to the fourth,
wherein the metamaterial (8) is designed to position shift the
electromagnetic sensor (7) towards a periphery of the tool body
(1).
[0075] In a sixth example, there is disclosed herein a method
according to any of the preceding examples first to the fifth,
wherein the electromagnetic sensor (7) is physically located away
from a central axis of the tool (1).
[0076] In a seventh example, there is disclosed herein a method
according to any of the preceding examples first to the sixth,
wherein the metamaterial (8) is designed to position shift the
electromagnetic sensor (7) towards a center of the tool body
(1).
[0077] In an eighth example, there is disclosed herein a method
according to any of the preceding examples first to the seventh,
wherein the metamaterial (8) is embedded in the tool body (1).
[0078] In a ninth example, there is disclosed herein a method
according to any of the preceding examples first to the eighth,
wherein the metamaterial (8) is coupled to the tool via a
deployable arm (5).
[0079] In a tenth example, there is disclosed herein a method
according to any of the preceding examples first to the ninth,
further including at least a second electromagnetic sensor (7a)
coupled to the metamaterial (8), where the first electromagnetic
sensor (7) is position shifted to a first position, and the second
electromagnetic sensor (7a) is position shifted to the first or to
the second position.
[0080] In an eleventh example, there is disclosed herein a method
according to any of the preceding examples first to the tenth,
where the third electromagnetic sensor (7b) is position shifted to
the first, to the second, or to a third position.
[0081] In a twelfth example, there is disclosed herein a method
according to any of the preceding examples first to the eleventh,
wherein the electromagnetic sensors (7) comprise a triaxial
coil.
[0082] In a thirteenth example, there is disclosed herein a method
according to any of the preceding examples first to the twelfth,
wherein the metamaterial (8) is designed to shrink the effective
size of the electromagnetic sensor (7).
[0083] In a fourteenth example, there is disclosed herein a method
according to any of the preceding examples first to the thirteenth,
wherein the electromagnetic sensor (7) comprises a coil.
[0084] In a fifteenth example, there is disclosed herein a method
according to any of the preceding examples first to the fourteenth,
wherein the electromagnetic sensor (7) comprises a coil.
[0085] In a sixteenth example, there is disclosed herein a method
of designing a well logging tool, including: constructing a
metamaterial (8) having unit cells in a configuration providing at
least one of a position-shifting function with respect to
electromagnetic radiation passing through the metamaterial (8), and
a size-shrinking function with respect to an electromagnetic sensor
(7); locating the electromagnetic sensor (7) in operative
relationship with the constructed metamaterial (8); and providing
the electromagnetic sensor (7) and metamaterial (8) in a tool body
(1).
[0086] In a seventeenth example, there is disclosed herein a method
according to the sixteenth, further comprising constructing the
metamaterial (8) having unit cells in a configuration providing
size scaling of said electromagnetic sensor (7).
[0087] In an eighteenth example, there is disclosed herein a method
according to the sixteenth or seventeenth examples, wherein the
metamaterial (8) is designed to position-shift the effective
location of the electromagnetic sensor (7) towards a periphery of
the tool body (1).
[0088] In a nineteenth example, there is disclosed herein a method
according to any of the examples from the sixteenth to the
eighteenth, wherein the electromagnetic sensor (7) is embedded in
the metamaterial (8).
[0089] In a twentieth example, there is disclosed herein A method
of designing a well logging tool, including: constructing a
metamaterial (8) having unit cells in a configuration providing a
size-shrinking function with respect to an electromagnetic sensor
(7); locating the electromagnetic sensor (7) in operative
relationship with the constructed metamaterial (8); and providing
the electromagnetic sensor (7) and metamaterial (8) in a tool body
(1).
[0090] The metamaterials disclosed in the present disclosure can be
designed according to the transformation optics rules disclosed in
detail above. In general, these transformation optics rules are
described by inhomogeneous anisotropic permittivity and
permeability tensors, whose values lie within the range of
electromagnetic frequencies used in operation of such measurement
tools.
[0091] The embodiments shown and described above are only examples.
Many details are often found in the art such as the other features
of a logging system. Therefore, many such details are neither shown
nor described. Even though numerous characteristics and advantages
of the present technology have been set forth in the foregoing
description, together with details of the structure and function of
the present disclosure, the disclosure is illustrative only, and
changes may be made in the detail, especially in matters of shape,
size and arrangement of the parts within the principles of the
present disclosure to the full extent indicated by the broad
general meaning of the terms used in the attached claims. It will
therefore be appreciated that the embodiments described above may
be modified within the scope of the appended claims.
* * * * *